**1. Introduction**

394 Biogas

Regulations on access to gas supply networks (Gas Network Access Ordinance - GasNZV)

electricity network tariff regulations of 8 April 2008.

of 25 July 2005, last amended by Regulation amending the Gas Network Access Ordinance, the gas network tariff regulations, the incentive regulations and the

> Biogas produced in anaerobic digesters consists of methane (50%–80%), carbon dioxide (20%–50%), and trace levels of other gases such as hydrogen, carbon monoxide, nitrogen, oxygen, and hydrogen sulfide. Anaerobic digestion is a biological process in which organic material is decomposed by bacteria in the absence of air. The general technology of anaerobic digestion of complex organic matter is well known and has been applied for over 60 years as part of domestic sewage treatment to stabilize organic wastes. Bal & Dhagat (2001) points out that the anaerobic process is more advantageous than the aerobic process in organic waste treatment because of the high degree of waste stabilization, low production of excess biological sludge, low nutrient requirement and production of methane gas as a useful byproduct. Several studies have been carried out for evaluating kinetic parameters and model equations for anaerobic digestion by Siles et al. (2010), Borja et al. (2005), Jimenez et al. (2004), Raposo et al. (2009), Rincon et al. (2009) and Hu et al. (2002); these are all based on the Monod kinetic model (Monod 1950) and on the revised kinetic model developed by Chen et al. (1980) and Hashimoto et al. (1981).

> In the microbiology of methanogenic process four different bacterial groups are identified as being responsible for carrying out the anaerobic digestion of complex organic matter. The first group of bacteria is hydrolytic bacteria which catabolizes carbohydrate, protein, lipid and other minor components of organic matter to fatty acids, H2 and CO2. The second group of bacteria is hydrogen producing acetogenic bacteria which catabolizes certain fatty acids and neutral end products to acetate, CO2 and H2. The third group of bacteria is homo acetogenic which synthesizes acetate using H2, CO2 and formate, and hydrolyzes multicarbon compound to acetic acid. Finally, the fourth group of bacteria i.e. methanogenic bacteria utilizes acetate, carbon dioxide and hydrogen to produce methane. The concerted action of these four bacterial groups ensures process stability during anaerobic digestion of the complex organic matter.

The reactions involved in these steps are given below:

• Phase-I. Solubilization of carbohydrate via hydrolysis

$$[\mathbf{C}\_{\theta}\mathbf{H}\_{10}\mathbf{O}\_{5}]\mathbf{u} + \eta\mathbf{H}\_{2}\mathbf{O} = \eta\mathbf{C}\_{\theta}\mathbf{H}\_{12}\mathbf{O}\_{6} \tag{1}$$

• Phase-II. Acidogenesis fermentation of glucose to acetate

Where

Where

concentration.

Kinetics of Biogas Production from Banana Stem Waste 397

<sup>=</sup> �

Eq. 12 shows that effluent substrate concentration depends on the influent substrate

The minimum retention time indicating when the washout of micro-organisms occurs is

�� <sup>=</sup> � ����

There are two different approaches generally used to study the kinetics of biogas production of lignocellulosic waste: one approach is to find the rate-limiting substrate for the kinetic evaluation; another approach is using chemical oxygen demand or volatile solids concentration as an indicator of the substrate concentration (Chen & Hashimoto, 1978). There are difficulties in using COD or VS as the gross substrate since a portion of the COD or VS is not available to the microbes as substrate. The laboratory test for COD of high strength residues requires at least 100 times dilution which generally yields unreliable data. Also, some of the volatile acids in the effluent are volatilised during the VS determination. Because the volatile acids are precursors of biogas production, their volatilisation during the

Biogas production is directly correlated with COD reduction. Since no oxidising agent is added, the only way COD reduction can occur is through the removal of organic material from the waste, such as through the evolution of methane and carbon dioxide. The other avenues of COD reduction through hydrogen sulpsulphide and hydrogen gas evolution are insignificant (Chen & Hashimoto, 1978). A reduction of 1 g COD is equivalent to the production of 0.35 l of methane at STP. Knowing the COD loading to the reactor and the

The biodegradable COD in the reactor will be directly proportional to (B0 − B) where B denotes the volume (in litres) of methane produced under normal conditions of pressure and temperature per gram of substrate (COD) added to the digester and B0 is the volume of methane produced under normal conditions of pressure and temperature per gram of substrate added at infinite retention time or for complete utilization of substrate and B0 will be directly proportional to the biodegradable COD loading (Chen & Hashimoto, 1978).

<sup>=</sup> �

<sup>+</sup> � ���� �

VS determinations causes errors in the calculated amount of substrate utilised.

volume of methane produced, the remaining COD in the digester can be calculated.

���� ��

θ = � ����

��������� (12)

(13)

��������� (14)

������ (15)

� ��

numerically equal to the reciprocal of the maximum growth rate:

μmax is the maximum specific microbial growth rate

β is a dimensionless kinetic parameter

K is an dimensionless kinetic parameter.

Therefore, from Eq. (12) one obtains:

From Eq. (14) one obtains:

$$\rm C\_6H\_{12}O\_6 + 2H\_2O = 2CH\_3COOH + 4H\_2 + 2CO\_2 \tag{2}$$

• Phase-III. Methanogenic reaction

$$\text{CH}\_3\text{COOH} = \text{CH}\_4 + \text{CO}\_2 \tag{3}$$

$$4\text{H}\_2 + \text{CO}\_2 = \text{CH}\_4 + 2\text{H}\_2\text{O} \tag{4}$$

#### **1.1 Chen–Hashimoto kinetic model of anaerobic digestion**

Chen–Hashimoto model was used for kinetic analysis of the experimental data. In a completely mixed continuous digester the rates of change of cell mass and substrate concentration are expressed by the following equations:

$$\frac{d\mathbf{X}}{dt} = \mu \mathbf{X} - \frac{\mathbf{x}}{\theta} \tag{5}$$

$$\frac{d\mathbf{S}}{dt} = -\mathbf{r} + \frac{\mathbf{s}\_0 - \mathbf{s}}{\theta} \tag{6}$$

Where

X is the concentration of cell mass

μ the specific microbial growth rate

θ the hydraulic retention time

S0 the concentration of substrate in the influent,

S the concentration of substrate in the effluent

r is the volumetric substrate utilisation rate

The relationship between r and μ is defined by the following equation:

$$
\mu = \frac{\text{yr}}{\text{x}}\tag{7}
$$

Where

Y is the yield coefficient (cell mass/substrate mass) and is considered constant (Chen & Hashimoto, 1978). In the steady-state, dX/dt = 0 and dS/dt = 0, hence

$$
\mu = \frac{1}{\theta} = \mathbf{D} \tag{8}
$$

Where D is the dilution rate

$$\mathbf{r} = \frac{\mathbf{s}\_{\theta} - \mathbf{s}}{\theta} \tag{9}$$

and

$$\mathbf{X} = \mathbf{Y}(\mathbf{S}\_0 - \mathbf{S}) \tag{10}$$

Substituting these expressions in Contois' equation:

$$
\mu = \frac{\mu\_{\text{max}}s}{\beta \text{x} + \text{s}} \tag{11}
$$

Where

396 Biogas

C6H12O6 + 2H2O = 2CH3COOH + 4H2 + 2CO2 (2)

CH3COOH = CH4 + CO2 (3)

4H2 + CO2 = CH4 + 2H2O (4)

Chen–Hashimoto model was used for kinetic analysis of the experimental data. In a completely mixed continuous digester the rates of change of cell mass and substrate

�� = μX − �

�� = −r + ����

μ = ��

Y is the yield coefficient (cell mass/substrate mass) and is considered constant (Chen &

μ = �

r = ����

μ = �����

�

(5)

� (6)

� (7)

� = D (8)

� (9)

���� (11)

X = Y(S� − S) (10)

��

��

The relationship between r and μ is defined by the following equation:

Hashimoto, 1978). In the steady-state, dX/dt = 0 and dS/dt = 0, hence

• Phase-III. Methanogenic reaction

X is the concentration of cell mass μ the specific microbial growth rate θ the hydraulic retention time

S0 the concentration of substrate in the influent, S the concentration of substrate in the effluent r is the volumetric substrate utilisation rate

Substituting these expressions in Contois' equation:

Where

Where

Where

and

D is the dilution rate

**1.1 Chen–Hashimoto kinetic model of anaerobic digestion** 

concentration are expressed by the following equations:

μmax is the maximum specific microbial growth rate β is a dimensionless kinetic parameter

$$\frac{\text{g}}{\text{g}} = \frac{\text{K}}{\mu\_{\text{max}} \text{e} - \text{1} + \text{K}} \tag{12}$$

Where

K is an dimensionless kinetic parameter.

Eq. 12 shows that effluent substrate concentration depends on the influent substrate concentration.

The minimum retention time indicating when the washout of micro-organisms occurs is numerically equal to the reciprocal of the maximum growth rate:

$$
\Theta\_{\rm min} = \frac{1}{\mu\_{\rm max}} \tag{13}
$$

There are two different approaches generally used to study the kinetics of biogas production of lignocellulosic waste: one approach is to find the rate-limiting substrate for the kinetic evaluation; another approach is using chemical oxygen demand or volatile solids concentration as an indicator of the substrate concentration (Chen & Hashimoto, 1978). There are difficulties in using COD or VS as the gross substrate since a portion of the COD or VS is not available to the microbes as substrate. The laboratory test for COD of high strength residues requires at least 100 times dilution which generally yields unreliable data. Also, some of the volatile acids in the effluent are volatilised during the VS determination. Because the volatile acids are precursors of biogas production, their volatilisation during the VS determinations causes errors in the calculated amount of substrate utilised.

Biogas production is directly correlated with COD reduction. Since no oxidising agent is added, the only way COD reduction can occur is through the removal of organic material from the waste, such as through the evolution of methane and carbon dioxide. The other avenues of COD reduction through hydrogen sulpsulphide and hydrogen gas evolution are insignificant (Chen & Hashimoto, 1978). A reduction of 1 g COD is equivalent to the production of 0.35 l of methane at STP. Knowing the COD loading to the reactor and the volume of methane produced, the remaining COD in the digester can be calculated.

The biodegradable COD in the reactor will be directly proportional to (B0 − B) where B denotes the volume (in litres) of methane produced under normal conditions of pressure and temperature per gram of substrate (COD) added to the digester and B0 is the volume of methane produced under normal conditions of pressure and temperature per gram of substrate added at infinite retention time or for complete utilization of substrate and B0 will be directly proportional to the biodegradable COD loading (Chen & Hashimoto, 1978). Therefore, from Eq. (12) one obtains:

$$\frac{\mathbf{B}\_0 - \mathbf{B}}{\mathbf{B}\_0} = \frac{\mathbf{K}}{\mu\_{\text{max}} \theta - 1 + \mathbf{K}} \tag{14}$$

From Eq. (14) one obtains:

$$
\Theta = \frac{1}{\mu\_{\text{max}}} + \frac{\text{K}}{\mu\_{\text{max}}} \frac{\text{B}}{(\text{B}\_{\text{0}} - \text{B})} \tag{15}
$$

Kinetics of Biogas Production from Banana Stem Waste 399

All experiments were done in 20 L anaerobic sequencing batch reactor followed by 10 L fixed bed reactor with gas outlet (Fig. 1). All the reactors were seeded with anaerobic acclimatized banana stem sludge. The anaerobic digestion system was varied at different reaction temperatures using water bath. The HRT and OLR for this system were 9 d and 4 g TS/l.d respectively. The process was conducted at ambient temperature for the first stage and thermophilic temperature for the second stage. Daily withdrawal of an appropriate volume from the reactor corresponding to the determined HRT or OLR was done by a draw-and-fill method. Biogas evolved from the fixed bed reactor was measured and collected in a gas holder by water displacement. Samples were collected and analyzed for

Fig. 1. Two-stages biogas production system

**2.2 Experimental set-up** 

performance evaluation.

Thus, by first calculating the value of B0, the graph of θ versus B/(B0−B) produces a straight line with an intercept of 1/μmax and with a slope of K/μmax. To obtain the parameter B0 one uses the following equation, which is easily derived from Eq. (14):

$$\mathbf{B} = \mathbf{B}\_0 \left| \mathbf{1} - \frac{\mathbf{K}}{\mu\_{\text{max}} \mathbf{e} - \mathbf{1} + \mathbf{K}} \right| \tag{16}$$

Since B is the methane production per gram of added COD, the volumetric methane production rate (δ) equals B multiplied by the loading rate:

$$\mathcal{S} = \frac{\mathcal{S}\_0}{\theta} = \frac{\mathcal{S}\_0 \mathcal{S}\_0}{\theta} \left| 1 - \frac{\mathcal{K}}{\mu\_{\text{max}} \theta - 1 + \mathcal{K}} \right| \tag{17}$$

Where

δ has the dimensions of volume methane per volume digester per unit time.

The objective of the present study is to develop kinetic parameters for two-stage biogas production using banana stem waste as substrate.
